by Sir William Thomson

“ A perfect thermodynamic engine of any kind is a machine by means of which the greatest possible amount of mechanical effect can be obtained from a given thermal agency; and, therefore, if in any manner we can construct or imagine a perfect engine which may be applied for the transference of a given quantity of heat from a body at any given temperature to another body at a lower given temperature, and if we can evaluate the mechanical effect thus obtained, we shall be able to answer the question at present under consideration, and so to complete the theory of the motive power of heat. ”

“ In the present state of science, however, no operation is known by which heat can be absorbed into a body without either elevating its temperature or becoming latent, and producing some alteration in its physical condition; and the fundamental axiom adopted by Carnot may be considered as still the most probable basis for an investigation of the motive power of heat; although this, and with it every other branch of the theory of heat, may ultimately require to be reconstructed upon another foundation, when our experimental data are more complete. ”

“ We are now led to the conclusion that the origin of motive power, developed by the alternate expansions and contractions of a body, must be found in the agency of heat entering the body and leaving it; since there cannot, at the end of a complete cycle, when the body is restored to its primitive physical condition, have been any absolute absorption of heat, and consequently no conversion of heat, or caloric, into mechanical effect ”

“ But whatever kind of engine we may consider with this view, it will be necessary for us to prove that it is a perfect engine; since the transference of the heat from one body to the other may be wholly, or partially, effected by conduction through a solid, [7] without the development of mechanical effect; and, consequently, engines may be constructed in which the whole or any portion of the thermal agency is wasted. Hence it is of primary importance to discover the criterion of a perfect engine. ”

“ Nothing can be lost in the operations of nature—no energy can be destroyed. What effect, then, is produced in place of the mechanical effect which is lost? A perfect theory of heat imperatively demands an answer to this question ”

“ For to "push the principle of expansion to the utmost," we must allow the steam, before leaving the cylinder, to expand until its pressure is the same as that of the vapor in the condenser. According to "Watt's law," its temperature would then be the same as (actually a little above, as Regnault has shown) that of the condenser, and hence the steam-engine worked in this most advantageous way has in reality the very fault that Watt found in Newcomen's engine. ”

“ In many of the actual phenomena of nature several or all of these effects are produced together; and their complication will, if we attempt to trace the agency of heat in producing any individual effect, give rise to much perplexity. ”

“ In p. 30 some conclusions drawn by Carnot from his general reasoning were noticed; according to which it appears, that if the value of μ for any temperature is known, certain information may be derived with reference to the saturated vapor of any liquid whatever, and, with reference to any gaseous mass, without the necessity of experimenting upon the specific medium considered. Nothing in the whole range of Natural Philosophy is more remarkable than the establishment of general laws by such a process of reasoning. ”

“ If, in place of compressing the air, we allow it to expand to two litres, four litres, eight litres, etc., it will be necessary to supply equal quantities of heat to maintain the temperature always at the same degree. ”

“ We have seen, however, that doubt may exist with reference to the truth of the axiom on which the entire theory is founded, and it therefore becomes more than a matter of mere curiosity to put the inferences deduced from it to the test of experience. ”

“ Besides these data, however, the density of saturated vapor must be known, in order that k, the latent heat of a unit of volume, may be calculated from Regnault's determination of the latent heat of a given weight. [18] Between the limits of 0° and 100°, it is probable, from various experiments which have been made, that the density of vapor follows very closely the simple laws which are so accurately verified by the ordinary gases; [19] and thus it may be calculated from Regnault's table giving the pressure at any temperature within those limits. ”

“ Joule of Manchester, that heat is evolved in every part of a closed electric conductor, moving in the neighborhood of a magnet, [5] that heat is generated by the friction of fluids in motion, seem to overturn the opinion commonly held that heat cannot be generated, but only produced from a source, where it has previously existed either in a sensible or in a latent condition. ”

“ Joule (at the conclusion of his paper "On the Changes of Temperature produced by the Rarefaction and Condensation of Air." Phil. Mag., May 1845, vol. xxvi.) If we do so, however, we meet with innumerable other difficulties—insuperable without farther experimental investigation, and an entire reconstruction of the theory of heat from its foundation. It is in reality to experiment that we must look—either for a verification of Carnot's axiom, and an explanation of the difficulty we have been considering; or for an entirely new basis of the Theory of Heat. ”

“ The diminution of volume in the third operation must be also equal to dv, or only differ from it by an infinitely small quantity of the second order. During the second operation we may suppose the volume to be increased by an infinitely small quantity φ; which will occasion a diminution of pressure and a diminution of temperature, denoted respectively by ω and τ. ”

“ CARNOT'S THEORY OF THE MOTIVE POWER OF HEAT. [2]
WITH NUMERICAL RESULTS DEDUCED FROM REGNAULT'S EXPERIMENTS ON STEAM. [3]
By Sir William Thomson [Lord Kelvin] .
1. The presence of heat may be recognized in every natural object; and there is scarcely an operation in nature which is not more or less affected by its all-pervading influence. An evolution and subsequent absorption of heat generally give rise to a variety of effects; among which may be enumerated, chemical combinations or decompositions; the fusion of solid substances ”

“ The actual average of work performed by good Cornish engines and boilers is 55,000,000 foot-pounds for each bushel of coal, or less than half the experimental performance of the Fowey Consols engine, more than half the actual duty performed by the United Mines engine in 1840 ”

“ This expression may be modified by employing the equations PV = P'V' = p0v0 (1 + Et) ; and we thus obtain
From this result we draw the following conclusion:
47. Equal volumes of all elastic fluids, taken at the same temperature and pressure, when compressed to smaller equal volumes, disengage equal quantities of heat.
This extremely remarkable theorem of Carnot's was independently laid down as a probable experimental law by Dulong, in his "Récherches sur la Chaleur Spécifique des Fluides Élastiques," and it therefore affords a most powerful confirmation of the theory. ”

“ Draw any line PP' parallel to OX, meeting the curvilinear sides of the quadrilateral in P and P'. Let ξ denote the length of this line, and p its distance from OX. The area of the figure, according to the integral calculus, will be denoted by the expression
where p1 and p3 (the limits of integration indicated according to Fourier's notation) denote the lines OA and N3A3, which represent respectively the pressures during the first and third operations. ”

“ With reference to the cases (3) , (4) , (6) , (7) , the hypothesis of Table B is probably in general nearer the truth than that of Table A. In (4) , (6) , and (7) , especially upon hypothesis B, there is much uncertainty as to the amount of evaporation that will be actually produced by 1 lb. of fuel. ”

“ This reasoning is, of course, founded on Carnot's fundamental principle, which is tacitly assumed in the commonly-received ideas connected with "Watt's law," the "latent heat of steam," and "the total heat of steam." ↑ Thus, from Carnot's calculations, we find, in the case of alcohol 4.035, and in the case of water 3.648, instead of 3.963 and 3.658, which are Clapeyron's results in the same cases. ↑ A still closer agreement must be expected when more accurate experimental data are afforded with reference to the other media. Mons. ”